A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells. (English) Zbl 1036.35053

Summary: In this paper, we investigate a linear population model of cells that are capable of simultaneous proliferation and maturation. We consider the case when the time required for a cell to divide depends on its maturity. This model is described by a first order partial differential system with a retardation of the maturation variable and a time delay depending on this maturity. Both delays are due to cell replication.


35F25 Initial value problems for nonlinear first-order PDEs
35L60 First-order nonlinear hyperbolic equations
92C37 Cell biology
92D25 Population dynamics (general)
35R10 Partial functional-differential equations
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